• Motivation for this study
• Upwelling patterns
• Common types of unsupervised image classification
  • PCA
  • K-means
  • Hierarchical clustering
• Seasonal patterns of upwelling revealed by image classification
• Changes in upwelling in the SEAS

2014-2019 NOAA Fisheries/India Ministry of Earth Sciences joint research on improving forecasts of the indian oil sardine

• Hugely important fishery for India.
• India fishery produces 66–96% (average 80%) of the global oil sardine catch.
• Southeastern Arabian Sea (Kerala) produces the vast majority of that.

Improving forecasts using environmental covariates: a case study on the Indian oil sardine (Sardinella longiceps), May 24th, UW Fish and Wildlife Ecology Seminars.

• Nutrient rich water brought to the surface
• Phytoplankton blooms
• Sea surface temperature (SST) differential: Cold water along the coast and warm water off-shore

Land warms faster than the ocean -> changes in coastal winds

Projected warming between 2015 and 2050

Di Lorenzo, E. 2015. The future of coastal ocean upwelling. Nature 518, 310–311.

…as opposed to other metrics of upwelling intensity.

• Patterns are changing so I am looking for things that haven’t been seen before
• I don’t know what I am looking for
• I am looking for novel patterns of upwelling

Three types of unsupervised image classification

• Principal Components Analysis (PCA) or Empirical Othogonal Factorization (EOF)
• K-means clustering
• Hierarchical clustering

Changes in the upwelling patterns in the SEAS

• As revealed by the image classification
• Changes to the pattern not absolute temperature
• Arabian Sea has warmed a lot in the past 2 decades. I have removed that by removing the mean from each image.

• An image has \(p\) pixels
• Each row is an image. Each column is a pixel.
• Get rid of the NA (land) columns. No NAs allowed otherwise.
• Values are temperature with the mean temperature in that image subtracted. In some applications, you would standardize the variance to 1.

Here are 5 images and just the first 10 pixels of the image.

##              p1    p2    p3    p4    p5    p6    p7    p8    p9   p10
## 1979-01-01 0.11  0.01 -0.08 -0.13 -0.16 -0.15 -0.12 -0.07 -0.04 -0.03
## 1979-02-01 0.19  0.10  0.03  0.00  0.02  0.08  0.12  0.15  0.16  0.15
## 1979-03-01 0.14  0.07  0.04  0.04  0.10  0.18  0.27  0.33  0.34  0.30
## 1979-04-01 0.14  0.09  0.04  0.01  0.02  0.05  0.09  0.11  0.08  0.03
## 1979-05-01 0.01 -0.02 -0.06 -0.08 -0.09 -0.06 -0.03 -0.02 -0.03 -0.05

• Each image (a data set with \(p\) variables) can be expressed as the weighted sum of orthogonal eigenvectors (i.e. independent).
• There are an infinite possible number of sets of eigenvectors. Usual idea is to pick ones that maximize the differention between images.

\[\text{image} = \alpha_1 \lambda_1 + \alpha_2 \lambda_2 + \alpha_3 \lambda_3 + \dots\]

Pacific Decadal Oscillation index is an example. It is the weighting (\(\alpha\)) on the first \(\lambda\) from gridded SST anomalies in the North Pacific.

sst.pca <- prcomp(X_norm, scale = FALSE, center=FALSE)

• The \(\lambda\) are in sst.pca$rotation with each column an “eigen image”.
• The \(\alpha\) are in sst.pca$x. One for each image and each \(\lambda\).

Eigen images. Just first 10 pixels of the image are shown.

round(t(sst.pca$rotation)[1:5, 1:10], digits=2)

##        p1    p2    p3    p4    p5    p6    p7    p8    p9   p10
## PC1  0.06  0.06  0.05  0.05  0.04  0.04  0.04  0.04  0.04  0.03
## PC2 -0.06 -0.06 -0.07 -0.07 -0.08 -0.08 -0.08 -0.07 -0.07 -0.07
## PC3  0.02  0.01  0.00 -0.01 -0.02 -0.01 -0.01  0.00  0.01  0.01
## PC4 -0.02 -0.02 -0.02 -0.02 -0.04 -0.05 -0.05 -0.06 -0.05 -0.04
## PC5  0.00  0.01  0.02  0.02  0.03  0.03  0.03  0.03  0.03  0.04

# if image is say 25x25
library(raster)
img <- as.raster(matrix(sst.pca$rotation[,1], byrow=TRUE, ncol=25))
plot(img)

## Warning: Currect projection of shape p_stack unknown. Long lat (epsg 4326)
## coordinates assumed.

\[\text{image} = \alpha_1 \lambda_1 + \alpha_2 \lambda_2 + \alpha_3 \lambda_3\]

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Use the first 10 dimensions.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'